idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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52,501 | Interpreting table 1 in clinical research papers | No, your table means that the mean of HbA1c is 7.7 (in %), and that the standard deviation (SD) is 1.5 (again in %). The range will usually be much wider than 6.2-9.2%.
To be honest, the table is a little confusing. If they write "mean $\pm$ SD" in the caption, they should also write "$7.7 \pm 1.5$" in the table. Or co... | Interpreting table 1 in clinical research papers | No, your table means that the mean of HbA1c is 7.7 (in %), and that the standard deviation (SD) is 1.5 (again in %). The range will usually be much wider than 6.2-9.2%.
To be honest, the table is a li | Interpreting table 1 in clinical research papers
No, your table means that the mean of HbA1c is 7.7 (in %), and that the standard deviation (SD) is 1.5 (again in %). The range will usually be much wider than 6.2-9.2%.
To be honest, the table is a little confusing. If they write "mean $\pm$ SD" in the caption, they shou... | Interpreting table 1 in clinical research papers
No, your table means that the mean of HbA1c is 7.7 (in %), and that the standard deviation (SD) is 1.5 (again in %). The range will usually be much wider than 6.2-9.2%.
To be honest, the table is a li |
52,502 | Interpreting table 1 in clinical research papers | The first line in your picture says "mean +/- SD" so it seems reasonable to assume, that the mean HbA1c was 7.7% with a standard deviation of 1.5% and the mean Cholesterol was 4.9mmol/L with a standard deviation of 1.0mmol/L
The standard deviation is the square root of the variance an thus a measure of the amount of va... | Interpreting table 1 in clinical research papers | The first line in your picture says "mean +/- SD" so it seems reasonable to assume, that the mean HbA1c was 7.7% with a standard deviation of 1.5% and the mean Cholesterol was 4.9mmol/L with a standar | Interpreting table 1 in clinical research papers
The first line in your picture says "mean +/- SD" so it seems reasonable to assume, that the mean HbA1c was 7.7% with a standard deviation of 1.5% and the mean Cholesterol was 4.9mmol/L with a standard deviation of 1.0mmol/L
The standard deviation is the square root of t... | Interpreting table 1 in clinical research papers
The first line in your picture says "mean +/- SD" so it seems reasonable to assume, that the mean HbA1c was 7.7% with a standard deviation of 1.5% and the mean Cholesterol was 4.9mmol/L with a standar |
52,503 | Minimum expectation | When $p$ increases, that means its cumulative distribution function
$$P(x) = \int_0^x p(x)\,\mathrm{d}x$$
is convex. Since $P(0)=0$ and $P(1)=1,$ the convexity implies the graph of $P$ lies on or below the line segment connecting $(0,0)$ and $(1,1),$ a segment that covers a triangular area of $1/2.$ (The graph is th... | Minimum expectation | When $p$ increases, that means its cumulative distribution function
$$P(x) = \int_0^x p(x)\,\mathrm{d}x$$
is convex. Since $P(0)=0$ and $P(1)=1,$ the convexity implies the graph of $P$ lies on or bel | Minimum expectation
When $p$ increases, that means its cumulative distribution function
$$P(x) = \int_0^x p(x)\,\mathrm{d}x$$
is convex. Since $P(0)=0$ and $P(1)=1,$ the convexity implies the graph of $P$ lies on or below the line segment connecting $(0,0)$ and $(1,1),$ a segment that covers a triangular area of $1/2.... | Minimum expectation
When $p$ increases, that means its cumulative distribution function
$$P(x) = \int_0^x p(x)\,\mathrm{d}x$$
is convex. Since $P(0)=0$ and $P(1)=1,$ the convexity implies the graph of $P$ lies on or bel |
52,504 | Minimum expectation | First, change the problem to say that the density is non-decreasing and piecewise constant. Solve that problem first and then return to this problem.
Suppose there is a density $f(x)$ that minimizes $EX$ where $n$ is a positive integer and for the integers $1 \le i \le n$ the density is constant and equal to $a_i$ on e... | Minimum expectation | First, change the problem to say that the density is non-decreasing and piecewise constant. Solve that problem first and then return to this problem.
Suppose there is a density $f(x)$ that minimizes $ | Minimum expectation
First, change the problem to say that the density is non-decreasing and piecewise constant. Solve that problem first and then return to this problem.
Suppose there is a density $f(x)$ that minimizes $EX$ where $n$ is a positive integer and for the integers $1 \le i \le n$ the density is constant and... | Minimum expectation
First, change the problem to say that the density is non-decreasing and piecewise constant. Solve that problem first and then return to this problem.
Suppose there is a density $f(x)$ that minimizes $ |
52,505 | P value as a measure of effect size? | You intuition is correct here --- although the p-value is not used as a measure of effect size, you are correct that in some tests, for a fixed sample size the distribution of the p-value is monotonically related to the effect size, and thus is implicitly a transformed estimator of the effect size. Generally speaking,... | P value as a measure of effect size? | You intuition is correct here --- although the p-value is not used as a measure of effect size, you are correct that in some tests, for a fixed sample size the distribution of the p-value is monotonic | P value as a measure of effect size?
You intuition is correct here --- although the p-value is not used as a measure of effect size, you are correct that in some tests, for a fixed sample size the distribution of the p-value is monotonically related to the effect size, and thus is implicitly a transformed estimator of ... | P value as a measure of effect size?
You intuition is correct here --- although the p-value is not used as a measure of effect size, you are correct that in some tests, for a fixed sample size the distribution of the p-value is monotonic |
52,506 | P value as a measure of effect size? | Let’s do two t-test examples.
In the first situation, we take $25$ observations and get a mean of $0.59218$ and variance of $1.891$. Running through the one-sample t-test calculations, we get a t-stat of $2.1532$ and a p-value of $0.04157$, significant at the legendary $0.05$-level.
In the second situation, we take $25... | P value as a measure of effect size? | Let’s do two t-test examples.
In the first situation, we take $25$ observations and get a mean of $0.59218$ and variance of $1.891$. Running through the one-sample t-test calculations, we get a t-stat | P value as a measure of effect size?
Let’s do two t-test examples.
In the first situation, we take $25$ observations and get a mean of $0.59218$ and variance of $1.891$. Running through the one-sample t-test calculations, we get a t-stat of $2.1532$ and a p-value of $0.04157$, significant at the legendary $0.05$-level.... | P value as a measure of effect size?
Let’s do two t-test examples.
In the first situation, we take $25$ observations and get a mean of $0.59218$ and variance of $1.891$. Running through the one-sample t-test calculations, we get a t-stat |
52,507 | P value as a measure of effect size? | If sample size is equal, t is a function of effect size, and p is a function of p. So higher effect size is associated with lower p.
I wouldn't say " lower p-value in the tests indicate higher effect". I might say larger effect sizes are associated with smaller p-values. But why would you take a measure that is fairly ... | P value as a measure of effect size? | If sample size is equal, t is a function of effect size, and p is a function of p. So higher effect size is associated with lower p.
I wouldn't say " lower p-value in the tests indicate higher effect" | P value as a measure of effect size?
If sample size is equal, t is a function of effect size, and p is a function of p. So higher effect size is associated with lower p.
I wouldn't say " lower p-value in the tests indicate higher effect". I might say larger effect sizes are associated with smaller p-values. But why wou... | P value as a measure of effect size?
If sample size is equal, t is a function of effect size, and p is a function of p. So higher effect size is associated with lower p.
I wouldn't say " lower p-value in the tests indicate higher effect" |
52,508 | P value as a measure of effect size? | The p-value is the probability that the chosen test statistic would be as large or larger than you observed from the data, given the null hypothesis.
Typically, our null hypothesis is something like "this population parameter is equal to this constant value" and our test statistic is generally chosen in a way that will... | P value as a measure of effect size? | The p-value is the probability that the chosen test statistic would be as large or larger than you observed from the data, given the null hypothesis.
Typically, our null hypothesis is something like " | P value as a measure of effect size?
The p-value is the probability that the chosen test statistic would be as large or larger than you observed from the data, given the null hypothesis.
Typically, our null hypothesis is something like "this population parameter is equal to this constant value" and our test statistic i... | P value as a measure of effect size?
The p-value is the probability that the chosen test statistic would be as large or larger than you observed from the data, given the null hypothesis.
Typically, our null hypothesis is something like " |
52,509 | P value as a measure of effect size? | P-values are used as a measure of effect size all the time.
The simplest way to express effect sizes are
The raw or absolute effect sizes, like a difference between means.
Some alternatives to express (relative) effect sizes are
Cohen's D, which expresses effect size relative to the pooled population variances
t-st... | P value as a measure of effect size? | P-values are used as a measure of effect size all the time.
The simplest way to express effect sizes are
The raw or absolute effect sizes, like a difference between means.
Some alternatives to expre | P value as a measure of effect size?
P-values are used as a measure of effect size all the time.
The simplest way to express effect sizes are
The raw or absolute effect sizes, like a difference between means.
Some alternatives to express (relative) effect sizes are
Cohen's D, which expresses effect size relative to ... | P value as a measure of effect size?
P-values are used as a measure of effect size all the time.
The simplest way to express effect sizes are
The raw or absolute effect sizes, like a difference between means.
Some alternatives to expre |
52,510 | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regression? | This is a cost-benefit problem (or equivalently, a profit-optimisation problem) that is not fully answered by the regression model. This kind of problem requires you to combine your statistical inference about the product sales with economic analysis. Generally this entails writing the profit function for the firm as... | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regr | This is a cost-benefit problem (or equivalently, a profit-optimisation problem) that is not fully answered by the regression model. This kind of problem requires you to combine your statistical infer | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regression?
This is a cost-benefit problem (or equivalently, a profit-optimisation problem) that is not fully answered by the regression model. This kind of problem requires you to combine your statistical inference about t... | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regr
This is a cost-benefit problem (or equivalently, a profit-optimisation problem) that is not fully answered by the regression model. This kind of problem requires you to combine your statistical infer |
52,511 | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regression? | I believe what you are asking here is if the linear regression coefficients can be interpreted causally, i.e. if they can be used to calculate the effects of a (hypothetical) intervention, where you would change certain predictors by a value X, and use the regression to calculate the increase in sales etc.
The basic an... | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regr | I believe what you are asking here is if the linear regression coefficients can be interpreted causally, i.e. if they can be used to calculate the effects of a (hypothetical) intervention, where you w | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regression?
I believe what you are asking here is if the linear regression coefficients can be interpreted causally, i.e. if they can be used to calculate the effects of a (hypothetical) intervention, where you would change ... | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regr
I believe what you are asking here is if the linear regression coefficients can be interpreted causally, i.e. if they can be used to calculate the effects of a (hypothetical) intervention, where you w |
52,512 | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regression? | I agree with the sentiment and can also imagine there are dangers assuming an equal functionality of a few variable regression model applied to a different region is entirely appropriate to base a decision to increase the number of sale representatives.
Having at one time actually being in a sales position, one must un... | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regr | I agree with the sentiment and can also imagine there are dangers assuming an equal functionality of a few variable regression model applied to a different region is entirely appropriate to base a dec | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regression?
I agree with the sentiment and can also imagine there are dangers assuming an equal functionality of a few variable regression model applied to a different region is entirely appropriate to base a decision to inc... | Can I make economic decisions (e.g., profit maximisation) using inferences from multiple linear regr
I agree with the sentiment and can also imagine there are dangers assuming an equal functionality of a few variable regression model applied to a different region is entirely appropriate to base a dec |
52,513 | Is there a statistical distribution whose values are bounded $[-1,1]$ and sum to 1? | Scaling a Dirichlet distribution
If you want a variable that is distributed like a Dirichlet distributed variable but with a different range then you can scale and shift (transform the variable). This is effectively rescaling the axes.
To get from $[0,1]$ to $[-1,1]$ you can multiply by 2 and subtract 1. That is, your ... | Is there a statistical distribution whose values are bounded $[-1,1]$ and sum to 1? | Scaling a Dirichlet distribution
If you want a variable that is distributed like a Dirichlet distributed variable but with a different range then you can scale and shift (transform the variable). This | Is there a statistical distribution whose values are bounded $[-1,1]$ and sum to 1?
Scaling a Dirichlet distribution
If you want a variable that is distributed like a Dirichlet distributed variable but with a different range then you can scale and shift (transform the variable). This is effectively rescaling the axes.
... | Is there a statistical distribution whose values are bounded $[-1,1]$ and sum to 1?
Scaling a Dirichlet distribution
If you want a variable that is distributed like a Dirichlet distributed variable but with a different range then you can scale and shift (transform the variable). This |
52,514 | Is there a statistical distribution whose values are bounded $[-1,1]$ and sum to 1? | If you really need the variables to sum to one, you could "force it" by dividing by the sum. That is, if $X_1, X_2, \cdots X_n$ are random variables, then the RVs
$$Z_i = \frac{X_i}{\sum_{i=1}^n X_i}$$
have the property that $\sum_{i=1}^nZ_i = 1$ (so long as $\sum X_i \neq 0$). This is easy to show.
$$\sum_{j=1}^n Z_j ... | Is there a statistical distribution whose values are bounded $[-1,1]$ and sum to 1? | If you really need the variables to sum to one, you could "force it" by dividing by the sum. That is, if $X_1, X_2, \cdots X_n$ are random variables, then the RVs
$$Z_i = \frac{X_i}{\sum_{i=1}^n X_i}$ | Is there a statistical distribution whose values are bounded $[-1,1]$ and sum to 1?
If you really need the variables to sum to one, you could "force it" by dividing by the sum. That is, if $X_1, X_2, \cdots X_n$ are random variables, then the RVs
$$Z_i = \frac{X_i}{\sum_{i=1}^n X_i}$$
have the property that $\sum_{i=1}... | Is there a statistical distribution whose values are bounded $[-1,1]$ and sum to 1?
If you really need the variables to sum to one, you could "force it" by dividing by the sum. That is, if $X_1, X_2, \cdots X_n$ are random variables, then the RVs
$$Z_i = \frac{X_i}{\sum_{i=1}^n X_i}$ |
52,515 | Can someone please explain how to read the unconfoundedness assumption. I'm unable to understand the symbols specifically the upside down "T" | Generally, that "upside down T" indicates orthogonality or independence (or unconfoundedness?) and I would interpret that notation as saying that the random vector $(Y_i(0), Y_i(1))$ is (conditionally) independent of the random variable $W$ given $X_i$, or more verbosely, conditioned on knowledge of $X_i$. If the rando... | Can someone please explain how to read the unconfoundedness assumption. I'm unable to understand the | Generally, that "upside down T" indicates orthogonality or independence (or unconfoundedness?) and I would interpret that notation as saying that the random vector $(Y_i(0), Y_i(1))$ is (conditionally | Can someone please explain how to read the unconfoundedness assumption. I'm unable to understand the symbols specifically the upside down "T"
Generally, that "upside down T" indicates orthogonality or independence (or unconfoundedness?) and I would interpret that notation as saying that the random vector $(Y_i(0), Y_i(... | Can someone please explain how to read the unconfoundedness assumption. I'm unable to understand the
Generally, that "upside down T" indicates orthogonality or independence (or unconfoundedness?) and I would interpret that notation as saying that the random vector $(Y_i(0), Y_i(1))$ is (conditionally |
52,516 | Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y-\mu_Y|)$ | Consider a Laplace distribution with scale parameter equal to $1$. One can compute that the MAD equals $1$, and the variance equals $2$.
Now consider a Normal distribution with arbitrary mean, and with variance equal to $1.9$. One can compute the MAD to be
$$\sqrt{\frac{1.9 \cdot 2}{\pi}} = \sqrt{\frac{3.8}{\pi}} > \s... | Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y | Consider a Laplace distribution with scale parameter equal to $1$. One can compute that the MAD equals $1$, and the variance equals $2$.
Now consider a Normal distribution with arbitrary mean, and wit | Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y-\mu_Y|)$
Consider a Laplace distribution with scale parameter equal to $1$. One can compute that the MAD equals $1$, and the variance equals $2$.
Now consider a Normal distribution with arbitrary mean, and with variance... | Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y
Consider a Laplace distribution with scale parameter equal to $1$. One can compute that the MAD equals $1$, and the variance equals $2$.
Now consider a Normal distribution with arbitrary mean, and wit |
52,517 | Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y-\mu_Y|)$ | Consider a discrete random variable $Y$ that, for some constants $M\in\mathbb{R}$ and $\epsilon\in [0, 1]$, takes the following values:
$$
Y = \left\{\begin{array} ~-M+\mu_Y & \text{w.p.}~\epsilon/2 \\ \mu_Y & \text{w.p.}~1-\epsilon \\ M+\mu_Y & \text{w.p.}~\epsilon/2\end{array}\right.
$$
Simple calculations show that ... | Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y | Consider a discrete random variable $Y$ that, for some constants $M\in\mathbb{R}$ and $\epsilon\in [0, 1]$, takes the following values:
$$
Y = \left\{\begin{array} ~-M+\mu_Y & \text{w.p.}~\epsilon/2 \ | Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y-\mu_Y|)$
Consider a discrete random variable $Y$ that, for some constants $M\in\mathbb{R}$ and $\epsilon\in [0, 1]$, takes the following values:
$$
Y = \left\{\begin{array} ~-M+\mu_Y & \text{w.p.}~\epsilon/2 \\ \mu_Y & ... | Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y
Consider a discrete random variable $Y$ that, for some constants $M\in\mathbb{R}$ and $\epsilon\in [0, 1]$, takes the following values:
$$
Y = \left\{\begin{array} ~-M+\mu_Y & \text{w.p.}~\epsilon/2 \ |
52,518 | What is the intuition behind the Metropolis-Hastings Algorithm? [duplicate] | How is the $q$ distribution (the proposal) related to the intractable
posterior? I don't see how $q$ popped out of nowhere.
The posterior is not intractable: $f(x)$ must be available (in a numerical sense) up to a multiplicative constant for the Metropolis-Hastings algorithm to apply. Otherwise, latent or auxiliary ... | What is the intuition behind the Metropolis-Hastings Algorithm? [duplicate] | How is the $q$ distribution (the proposal) related to the intractable
posterior? I don't see how $q$ popped out of nowhere.
The posterior is not intractable: $f(x)$ must be available (in a numerica | What is the intuition behind the Metropolis-Hastings Algorithm? [duplicate]
How is the $q$ distribution (the proposal) related to the intractable
posterior? I don't see how $q$ popped out of nowhere.
The posterior is not intractable: $f(x)$ must be available (in a numerical sense) up to a multiplicative constant for... | What is the intuition behind the Metropolis-Hastings Algorithm? [duplicate]
How is the $q$ distribution (the proposal) related to the intractable
posterior? I don't see how $q$ popped out of nowhere.
The posterior is not intractable: $f(x)$ must be available (in a numerica |
52,519 | What is the intuition behind the Metropolis-Hastings Algorithm? [duplicate] | Ok. Let's starting by addressing your question piecemeal. First, how is $q$, called the jumping distribution chosen? It's up to you, the model-er. A reasonable assumption, as always, would be a Gaussian, but this may change according to the problem at hand. The choice of the jumping distribution will change how you wal... | What is the intuition behind the Metropolis-Hastings Algorithm? [duplicate] | Ok. Let's starting by addressing your question piecemeal. First, how is $q$, called the jumping distribution chosen? It's up to you, the model-er. A reasonable assumption, as always, would be a Gaussi | What is the intuition behind the Metropolis-Hastings Algorithm? [duplicate]
Ok. Let's starting by addressing your question piecemeal. First, how is $q$, called the jumping distribution chosen? It's up to you, the model-er. A reasonable assumption, as always, would be a Gaussian, but this may change according to the pro... | What is the intuition behind the Metropolis-Hastings Algorithm? [duplicate]
Ok. Let's starting by addressing your question piecemeal. First, how is $q$, called the jumping distribution chosen? It's up to you, the model-er. A reasonable assumption, as always, would be a Gaussi |
52,520 | the rules of "approximately independent" | The rule you outlined is the rule used for something being approximately independent. This is for when the sample is taken without replacement. Consider that if you sample a population randomly with replacement (so that it's possible you can pick the same person twice) this sample is taken completely randomly and fairl... | the rules of "approximately independent" | The rule you outlined is the rule used for something being approximately independent. This is for when the sample is taken without replacement. Consider that if you sample a population randomly with r | the rules of "approximately independent"
The rule you outlined is the rule used for something being approximately independent. This is for when the sample is taken without replacement. Consider that if you sample a population randomly with replacement (so that it's possible you can pick the same person twice) this samp... | the rules of "approximately independent"
The rule you outlined is the rule used for something being approximately independent. This is for when the sample is taken without replacement. Consider that if you sample a population randomly with r |
52,521 | the rules of "approximately independent" | It's a widely recognized rule for sampling without replacement. The intuition behind this rule is that in the 10% case even after drawing an element of the population the probability for the next element does not change so much that we simply neglect it. E.g.:
Let's say we have 100 Persons, then the first we ask has a ... | the rules of "approximately independent" | It's a widely recognized rule for sampling without replacement. The intuition behind this rule is that in the 10% case even after drawing an element of the population the probability for the next elem | the rules of "approximately independent"
It's a widely recognized rule for sampling without replacement. The intuition behind this rule is that in the 10% case even after drawing an element of the population the probability for the next element does not change so much that we simply neglect it. E.g.:
Let's say we have ... | the rules of "approximately independent"
It's a widely recognized rule for sampling without replacement. The intuition behind this rule is that in the 10% case even after drawing an element of the population the probability for the next elem |
52,522 | the rules of "approximately independent" | $\newcommand{\Z}{\mathbf Z}$$\newcommand{\y}{\mathbf y}$This sounds like this is a question about finite populations. Suppose we have a population $\mathscr U = \{1, \dots, N\}$ and each unit has a value $y_i$ associated with it. If we are taking a sample and using design-based inference we will need to consider
$$
\pi... | the rules of "approximately independent" | $\newcommand{\Z}{\mathbf Z}$$\newcommand{\y}{\mathbf y}$This sounds like this is a question about finite populations. Suppose we have a population $\mathscr U = \{1, \dots, N\}$ and each unit has a va | the rules of "approximately independent"
$\newcommand{\Z}{\mathbf Z}$$\newcommand{\y}{\mathbf y}$This sounds like this is a question about finite populations. Suppose we have a population $\mathscr U = \{1, \dots, N\}$ and each unit has a value $y_i$ associated with it. If we are taking a sample and using design-based ... | the rules of "approximately independent"
$\newcommand{\Z}{\mathbf Z}$$\newcommand{\y}{\mathbf y}$This sounds like this is a question about finite populations. Suppose we have a population $\mathscr U = \{1, \dots, N\}$ and each unit has a va |
52,523 | What methods can be used for distribution generation other than GANs? | There are many popular classes of generative models.
Autoregressive models: Here we model $\log p(x)$ as a sum of conditional terms $\sum_i \log p(x_i | x_{j < i})$. This group includes most natural language models, Transformers, PixelRNN, PixelCNN, and Wavenet. Can be used for image, text, sound, and almost any other ... | What methods can be used for distribution generation other than GANs? | There are many popular classes of generative models.
Autoregressive models: Here we model $\log p(x)$ as a sum of conditional terms $\sum_i \log p(x_i | x_{j < i})$. This group includes most natural l | What methods can be used for distribution generation other than GANs?
There are many popular classes of generative models.
Autoregressive models: Here we model $\log p(x)$ as a sum of conditional terms $\sum_i \log p(x_i | x_{j < i})$. This group includes most natural language models, Transformers, PixelRNN, PixelCNN, ... | What methods can be used for distribution generation other than GANs?
There are many popular classes of generative models.
Autoregressive models: Here we model $\log p(x)$ as a sum of conditional terms $\sum_i \log p(x_i | x_{j < i})$. This group includes most natural l |
52,524 | What methods can be used for distribution generation other than GANs? | The other large class of models that can do that are Variational Autoencoders.
Basically, they explicitly try to parameterize some specified probability distribution (up to you what it is) with one half of your neural network so that the parameters match your specification AND that the samples from that distribution c... | What methods can be used for distribution generation other than GANs? | The other large class of models that can do that are Variational Autoencoders.
Basically, they explicitly try to parameterize some specified probability distribution (up to you what it is) with one h | What methods can be used for distribution generation other than GANs?
The other large class of models that can do that are Variational Autoencoders.
Basically, they explicitly try to parameterize some specified probability distribution (up to you what it is) with one half of your neural network so that the parameters ... | What methods can be used for distribution generation other than GANs?
The other large class of models that can do that are Variational Autoencoders.
Basically, they explicitly try to parameterize some specified probability distribution (up to you what it is) with one h |
52,525 | What methods can be used for distribution generation other than GANs? | Yes, there are. Goodfellow's GAN tutorial lists a taxonomy of such methods.
Some example approaches that fall into Maximum Likelihood category:
autoregressive methods. Use $p_{\theta}(x) = \prod_{i} p(x_i|(x_j)_{j<1:i})$. Example: Pixel-Recurrent NN.
variational methods. Use $p_{\theta}(x) = \int p(x|z) p(z) dz$ Where... | What methods can be used for distribution generation other than GANs? | Yes, there are. Goodfellow's GAN tutorial lists a taxonomy of such methods.
Some example approaches that fall into Maximum Likelihood category:
autoregressive methods. Use $p_{\theta}(x) = \prod_{i} | What methods can be used for distribution generation other than GANs?
Yes, there are. Goodfellow's GAN tutorial lists a taxonomy of such methods.
Some example approaches that fall into Maximum Likelihood category:
autoregressive methods. Use $p_{\theta}(x) = \prod_{i} p(x_i|(x_j)_{j<1:i})$. Example: Pixel-Recurrent NN... | What methods can be used for distribution generation other than GANs?
Yes, there are. Goodfellow's GAN tutorial lists a taxonomy of such methods.
Some example approaches that fall into Maximum Likelihood category:
autoregressive methods. Use $p_{\theta}(x) = \prod_{i} |
52,526 | Polynomial Chebyshev Regression versus multi-linear regression | I think you have misunderstood the motivation for Chebyshev polynomials. Chebyshev polynomials are not used for statistical modelling at all --- their purpose is quite different. Chebyshev polynomials are a good and convenient solution to the classic numerical interpolation problem. Suppose I want to approximate a gene... | Polynomial Chebyshev Regression versus multi-linear regression | I think you have misunderstood the motivation for Chebyshev polynomials. Chebyshev polynomials are not used for statistical modelling at all --- their purpose is quite different. Chebyshev polynomials | Polynomial Chebyshev Regression versus multi-linear regression
I think you have misunderstood the motivation for Chebyshev polynomials. Chebyshev polynomials are not used for statistical modelling at all --- their purpose is quite different. Chebyshev polynomials are a good and convenient solution to the classic numeri... | Polynomial Chebyshev Regression versus multi-linear regression
I think you have misunderstood the motivation for Chebyshev polynomials. Chebyshev polynomials are not used for statistical modelling at all --- their purpose is quite different. Chebyshev polynomials |
52,527 | What is the difference between first order difference and moving average? | Suppose you have a set of time-series data values $x_1,...,x_n$. For some value $k<n$ in the series, the corresponding moving average over $k$ periods up to time $t$ is:
$$\bar{x}_{t}^{(k)} = \frac{1}{k} \sum_{i=0}^{k-1} x_{t-i}.$$
As you change the last time period $t$ you move the average to be an average over diffe... | What is the difference between first order difference and moving average? | Suppose you have a set of time-series data values $x_1,...,x_n$. For some value $k<n$ in the series, the corresponding moving average over $k$ periods up to time $t$ is:
$$\bar{x}_{t}^{(k)} = \frac{1 | What is the difference between first order difference and moving average?
Suppose you have a set of time-series data values $x_1,...,x_n$. For some value $k<n$ in the series, the corresponding moving average over $k$ periods up to time $t$ is:
$$\bar{x}_{t}^{(k)} = \frac{1}{k} \sum_{i=0}^{k-1} x_{t-i}.$$
As you change... | What is the difference between first order difference and moving average?
Suppose you have a set of time-series data values $x_1,...,x_n$. For some value $k<n$ in the series, the corresponding moving average over $k$ periods up to time $t$ is:
$$\bar{x}_{t}^{(k)} = \frac{1 |
52,528 | What is the difference between first order difference and moving average? | First I talk about first order difference
First order difference: To run most time series regressions stationary is essential condition. If your data is not stationary then we use differencing.When we deduct present observation from it's lag it's called first order difference. To run whether MA or AR or ARMA you shoul... | What is the difference between first order difference and moving average? | First I talk about first order difference
First order difference: To run most time series regressions stationary is essential condition. If your data is not stationary then we use differencing.When w | What is the difference between first order difference and moving average?
First I talk about first order difference
First order difference: To run most time series regressions stationary is essential condition. If your data is not stationary then we use differencing.When we deduct present observation from it's lag it'... | What is the difference between first order difference and moving average?
First I talk about first order difference
First order difference: To run most time series regressions stationary is essential condition. If your data is not stationary then we use differencing.When w |
52,529 | Minimum sample size for Spearman's correlation and Kendall's Tau b | For the purposes of a hypothesis test, there are two related approaches to finding an optimal sample size that are viable if you're willing to assume bivariate normality.
Power
To estimate minimal sample size at a given confidence level ($1-\alpha$) and power ($1-\beta$), we can use a modification of the equation for ... | Minimum sample size for Spearman's correlation and Kendall's Tau b | For the purposes of a hypothesis test, there are two related approaches to finding an optimal sample size that are viable if you're willing to assume bivariate normality.
Power
To estimate minimal sa | Minimum sample size for Spearman's correlation and Kendall's Tau b
For the purposes of a hypothesis test, there are two related approaches to finding an optimal sample size that are viable if you're willing to assume bivariate normality.
Power
To estimate minimal sample size at a given confidence level ($1-\alpha$) an... | Minimum sample size for Spearman's correlation and Kendall's Tau b
For the purposes of a hypothesis test, there are two related approaches to finding an optimal sample size that are viable if you're willing to assume bivariate normality.
Power
To estimate minimal sa |
52,530 | Is age categorical or quantitative or both? | Generally speaking, you should treat age as a quantitative variable, assuming you have the actual ages and not age brackets. There are several reasons for this. Perhaps most importantly, if you use age as a categorical variable, you typically would need $c-1$ variables to represent the age categories, $c$, in a regre... | Is age categorical or quantitative or both? | Generally speaking, you should treat age as a quantitative variable, assuming you have the actual ages and not age brackets. There are several reasons for this. Perhaps most importantly, if you use | Is age categorical or quantitative or both?
Generally speaking, you should treat age as a quantitative variable, assuming you have the actual ages and not age brackets. There are several reasons for this. Perhaps most importantly, if you use age as a categorical variable, you typically would need $c-1$ variables to r... | Is age categorical or quantitative or both?
Generally speaking, you should treat age as a quantitative variable, assuming you have the actual ages and not age brackets. There are several reasons for this. Perhaps most importantly, if you use |
52,531 | Is age categorical or quantitative or both? | I do not think it's a very good idea to categorize age in this way. This is not only for statistical reasons, but also because the outcome has only limited value: your output states, that a 39 year old person has a lesser risk than a 38 or 40 year old person. I guess the general interpretation - that age lowers the ris... | Is age categorical or quantitative or both? | I do not think it's a very good idea to categorize age in this way. This is not only for statistical reasons, but also because the outcome has only limited value: your output states, that a 39 year ol | Is age categorical or quantitative or both?
I do not think it's a very good idea to categorize age in this way. This is not only for statistical reasons, but also because the outcome has only limited value: your output states, that a 39 year old person has a lesser risk than a 38 or 40 year old person. I guess the gene... | Is age categorical or quantitative or both?
I do not think it's a very good idea to categorize age in this way. This is not only for statistical reasons, but also because the outcome has only limited value: your output states, that a 39 year ol |
52,532 | How to use press statistic for model selection | You calculate PRESS on a model trained on $n$ values to get an idea of its out-of-sample performance, by leaving out one sample at a time. So while you indeed end up with $n$ models to determine the statistic, you eventually use the original model trained on all $n$ values.
Since you are only leaving out a single obser... | How to use press statistic for model selection | You calculate PRESS on a model trained on $n$ values to get an idea of its out-of-sample performance, by leaving out one sample at a time. So while you indeed end up with $n$ models to determine the s | How to use press statistic for model selection
You calculate PRESS on a model trained on $n$ values to get an idea of its out-of-sample performance, by leaving out one sample at a time. So while you indeed end up with $n$ models to determine the statistic, you eventually use the original model trained on all $n$ values... | How to use press statistic for model selection
You calculate PRESS on a model trained on $n$ values to get an idea of its out-of-sample performance, by leaving out one sample at a time. So while you indeed end up with $n$ models to determine the s |
52,533 | How to use press statistic for model selection | "My confusion lies in the fact that a new regression equation (hence a new model) is estimated each time a data point is dropped"
This usually isn't the case, at least for standard [ridge-] regression models; you don't actually create a new model each time, but instead can work out what the output of that model would b... | How to use press statistic for model selection | "My confusion lies in the fact that a new regression equation (hence a new model) is estimated each time a data point is dropped"
This usually isn't the case, at least for standard [ridge-] regression | How to use press statistic for model selection
"My confusion lies in the fact that a new regression equation (hence a new model) is estimated each time a data point is dropped"
This usually isn't the case, at least for standard [ridge-] regression models; you don't actually create a new model each time, but instead can... | How to use press statistic for model selection
"My confusion lies in the fact that a new regression equation (hence a new model) is estimated each time a data point is dropped"
This usually isn't the case, at least for standard [ridge-] regression |
52,534 | Why is my p-value correlated to difference between means in two sample tests? | As you said, the p-value is uniformly distributed under the null hypothesis. That is, if the null hypothesis is really true, then upon repeated experiments we expect to find a fully random, flat distribution of p-values between [0, 1]. Consequently, a frequentist p-value says nothing about how likely the null hypothesi... | Why is my p-value correlated to difference between means in two sample tests? | As you said, the p-value is uniformly distributed under the null hypothesis. That is, if the null hypothesis is really true, then upon repeated experiments we expect to find a fully random, flat distr | Why is my p-value correlated to difference between means in two sample tests?
As you said, the p-value is uniformly distributed under the null hypothesis. That is, if the null hypothesis is really true, then upon repeated experiments we expect to find a fully random, flat distribution of p-values between [0, 1]. Conseq... | Why is my p-value correlated to difference between means in two sample tests?
As you said, the p-value is uniformly distributed under the null hypothesis. That is, if the null hypothesis is really true, then upon repeated experiments we expect to find a fully random, flat distr |
52,535 | Why is my p-value correlated to difference between means in two sample tests? | Why would you expect anything else? You don't need a simulation to know this is going to happen. Look at the formula for the t-statistic:
$t = \frac{\bar{x_1} - \bar{x_2} }{\sqrt{ \frac{s^2_1}{n_1} + \frac{s^2_2}{n_2} }}$
Obviously if you increase the true difference of means you expect $\bar{x_1} - \bar{x_2}$ will be... | Why is my p-value correlated to difference between means in two sample tests? | Why would you expect anything else? You don't need a simulation to know this is going to happen. Look at the formula for the t-statistic:
$t = \frac{\bar{x_1} - \bar{x_2} }{\sqrt{ \frac{s^2_1}{n_1} + | Why is my p-value correlated to difference between means in two sample tests?
Why would you expect anything else? You don't need a simulation to know this is going to happen. Look at the formula for the t-statistic:
$t = \frac{\bar{x_1} - \bar{x_2} }{\sqrt{ \frac{s^2_1}{n_1} + \frac{s^2_2}{n_2} }}$
Obviously if you in... | Why is my p-value correlated to difference between means in two sample tests?
Why would you expect anything else? You don't need a simulation to know this is going to happen. Look at the formula for the t-statistic:
$t = \frac{\bar{x_1} - \bar{x_2} }{\sqrt{ \frac{s^2_1}{n_1} + |
52,536 | Why is my p-value correlated to difference between means in two sample tests? | You should indeed not interpret the p-value as a probability that the null hypothesis is true.
However, a higher p-value does relate to stronger support for the null hypothesis.
Considering p-values as a random variable
You could consider p-values as a transformation of your statistic. See for instance the secondary x... | Why is my p-value correlated to difference between means in two sample tests? | You should indeed not interpret the p-value as a probability that the null hypothesis is true.
However, a higher p-value does relate to stronger support for the null hypothesis.
Considering p-values | Why is my p-value correlated to difference between means in two sample tests?
You should indeed not interpret the p-value as a probability that the null hypothesis is true.
However, a higher p-value does relate to stronger support for the null hypothesis.
Considering p-values as a random variable
You could consider p-... | Why is my p-value correlated to difference between means in two sample tests?
You should indeed not interpret the p-value as a probability that the null hypothesis is true.
However, a higher p-value does relate to stronger support for the null hypothesis.
Considering p-values |
52,537 | Transforming data with positive, negative, and zero values | Yes, you can add a constant and then take a logs.
There are many ways to transform data.
There is nothing inherently invalid about doing this, but very often such transformations are misguided. It is not necessary for the dependent variable to be normally distributed. The assumption about normality concerns the residua... | Transforming data with positive, negative, and zero values | Yes, you can add a constant and then take a logs.
There are many ways to transform data.
There is nothing inherently invalid about doing this, but very often such transformations are misguided. It is | Transforming data with positive, negative, and zero values
Yes, you can add a constant and then take a logs.
There are many ways to transform data.
There is nothing inherently invalid about doing this, but very often such transformations are misguided. It is not necessary for the dependent variable to be normally distr... | Transforming data with positive, negative, and zero values
Yes, you can add a constant and then take a logs.
There are many ways to transform data.
There is nothing inherently invalid about doing this, but very often such transformations are misguided. It is |
52,538 | Transforming data with positive, negative, and zero values | In the case of negative values, you can use the PowerTransformer(method='yeo-johnson') method from sklearn. It is capable of handling positive and negative values, also values of zero. The skewness (measure of normality) of the data should decrease substantially. As with any transform, you should use fit and transform ... | Transforming data with positive, negative, and zero values | In the case of negative values, you can use the PowerTransformer(method='yeo-johnson') method from sklearn. It is capable of handling positive and negative values, also values of zero. The skewness (m | Transforming data with positive, negative, and zero values
In the case of negative values, you can use the PowerTransformer(method='yeo-johnson') method from sklearn. It is capable of handling positive and negative values, also values of zero. The skewness (measure of normality) of the data should decrease substantiall... | Transforming data with positive, negative, and zero values
In the case of negative values, you can use the PowerTransformer(method='yeo-johnson') method from sklearn. It is capable of handling positive and negative values, also values of zero. The skewness (m |
52,539 | Transforming data with positive, negative, and zero values | In principle, transformations possible with variables that may be negative, zero or positive include
$\text{sign}(x) \log(1 + |x|)$, which conveniently preserves the sign of its argument (including mapping $0$ to $0$) while behaving like $\log x$ for $x \gg 0$ and like $-\log(- x)$ for $x \ll 0$.
Inverse hyperbolic ... | Transforming data with positive, negative, and zero values | In principle, transformations possible with variables that may be negative, zero or positive include
$\text{sign}(x) \log(1 + |x|)$, which conveniently preserves the sign of its argument (including | Transforming data with positive, negative, and zero values
In principle, transformations possible with variables that may be negative, zero or positive include
$\text{sign}(x) \log(1 + |x|)$, which conveniently preserves the sign of its argument (including mapping $0$ to $0$) while behaving like $\log x$ for $x \gg 0... | Transforming data with positive, negative, and zero values
In principle, transformations possible with variables that may be negative, zero or positive include
$\text{sign}(x) \log(1 + |x|)$, which conveniently preserves the sign of its argument (including |
52,540 | Regression predictions show far less variance than expected | Your training data - just as any other data - is a mixture of signal and noise. In modeling, we try to capture the signal, since the noise is by definition not predictable, except in a probabilistic sense.
predict.zeroinfl() by default predicts the expected response, i.e., the signal. Since the noise is mainly variatio... | Regression predictions show far less variance than expected | Your training data - just as any other data - is a mixture of signal and noise. In modeling, we try to capture the signal, since the noise is by definition not predictable, except in a probabilistic s | Regression predictions show far less variance than expected
Your training data - just as any other data - is a mixture of signal and noise. In modeling, we try to capture the signal, since the noise is by definition not predictable, except in a probabilistic sense.
predict.zeroinfl() by default predicts the expected re... | Regression predictions show far less variance than expected
Your training data - just as any other data - is a mixture of signal and noise. In modeling, we try to capture the signal, since the noise is by definition not predictable, except in a probabilistic s |
52,541 | Is a kernel function basically just a mapping? | My initial understanding is that a kernel is essentially just a
mapping into a higher dimension.
No. Kernel is a function that calculates dot product in the image of this mapping.
It can be thought of as defining dot product, using dot product from another space, where the mapping into this (often higher-dimensional... | Is a kernel function basically just a mapping? | My initial understanding is that a kernel is essentially just a
mapping into a higher dimension.
No. Kernel is a function that calculates dot product in the image of this mapping.
It can be thought | Is a kernel function basically just a mapping?
My initial understanding is that a kernel is essentially just a
mapping into a higher dimension.
No. Kernel is a function that calculates dot product in the image of this mapping.
It can be thought of as defining dot product, using dot product from another space, where ... | Is a kernel function basically just a mapping?
My initial understanding is that a kernel is essentially just a
mapping into a higher dimension.
No. Kernel is a function that calculates dot product in the image of this mapping.
It can be thought |
52,542 | Is a kernel function basically just a mapping? | My answer may be paraphrasing what you already gathered in the other threads, but here's my way of seeing this.
Technically, the kernel trick can indeed be seen as a mapping to a higher dimension (possibly infinite) where a linear method works. But it is much more than that, because you use an implicit definition of th... | Is a kernel function basically just a mapping? | My answer may be paraphrasing what you already gathered in the other threads, but here's my way of seeing this.
Technically, the kernel trick can indeed be seen as a mapping to a higher dimension (pos | Is a kernel function basically just a mapping?
My answer may be paraphrasing what you already gathered in the other threads, but here's my way of seeing this.
Technically, the kernel trick can indeed be seen as a mapping to a higher dimension (possibly infinite) where a linear method works. But it is much more than tha... | Is a kernel function basically just a mapping?
My answer may be paraphrasing what you already gathered in the other threads, but here's my way of seeing this.
Technically, the kernel trick can indeed be seen as a mapping to a higher dimension (pos |
52,543 | Why does changing random seeds alter results? | tl;dr practically speaking, you can probably set the seed to anything you want (e.g. your birthday or phone number [although there are obvious privacy issues there :-)] or your lucky number); with some interesting caveats, you can use the same random number seed for most of your analyses (I often use 1001). In order to... | Why does changing random seeds alter results? | tl;dr practically speaking, you can probably set the seed to anything you want (e.g. your birthday or phone number [although there are obvious privacy issues there :-)] or your lucky number); with som | Why does changing random seeds alter results?
tl;dr practically speaking, you can probably set the seed to anything you want (e.g. your birthday or phone number [although there are obvious privacy issues there :-)] or your lucky number); with some interesting caveats, you can use the same random number seed for most of... | Why does changing random seeds alter results?
tl;dr practically speaking, you can probably set the seed to anything you want (e.g. your birthday or phone number [although there are obvious privacy issues there :-)] or your lucky number); with som |
52,544 | Why bootstrapping? | Welcome to CV!
In bootstrapping, you repeatedly take samples with replacement from the original sample. The general idea behind this is that if you can estimate the uncertainty in your sample by asking the question: What if I didn't observe this observation, or that one, or if I observed this observation more than onc... | Why bootstrapping? | Welcome to CV!
In bootstrapping, you repeatedly take samples with replacement from the original sample. The general idea behind this is that if you can estimate the uncertainty in your sample by aski | Why bootstrapping?
Welcome to CV!
In bootstrapping, you repeatedly take samples with replacement from the original sample. The general idea behind this is that if you can estimate the uncertainty in your sample by asking the question: What if I didn't observe this observation, or that one, or if I observed this observ... | Why bootstrapping?
Welcome to CV!
In bootstrapping, you repeatedly take samples with replacement from the original sample. The general idea behind this is that if you can estimate the uncertainty in your sample by aski |
52,545 | Why bootstrapping? | I understood that bootstrapping is a technique used to estimate statistics of a population.
It is a technique mainly used
to estimate the standard error of an estimator of a population parameter $\theta$ and/or
to derive confidence intervals for $\theta$
in situations where these figures are too difficult to derive ... | Why bootstrapping? | I understood that bootstrapping is a technique used to estimate statistics of a population.
It is a technique mainly used
to estimate the standard error of an estimator of a population parameter $\t | Why bootstrapping?
I understood that bootstrapping is a technique used to estimate statistics of a population.
It is a technique mainly used
to estimate the standard error of an estimator of a population parameter $\theta$ and/or
to derive confidence intervals for $\theta$
in situations where these figures are too d... | Why bootstrapping?
I understood that bootstrapping is a technique used to estimate statistics of a population.
It is a technique mainly used
to estimate the standard error of an estimator of a population parameter $\t |
52,546 | How to test for difference in means between 5 groups? The variance between the groups are not equal. If they were equal, then I could use ANOVA | I would like to recommend generalized least squares as an option. Same way you can create a model for the mean of the data given your predictors, you can also create a model for variance. The gls() function in the nlme package permits us to do this.
I will demo how below:
set.seed(1984)
n <- 25
# Create heteroskedastic... | How to test for difference in means between 5 groups? The variance between the groups are not equal. | I would like to recommend generalized least squares as an option. Same way you can create a model for the mean of the data given your predictors, you can also create a model for variance. The gls() fu | How to test for difference in means between 5 groups? The variance between the groups are not equal. If they were equal, then I could use ANOVA
I would like to recommend generalized least squares as an option. Same way you can create a model for the mean of the data given your predictors, you can also create a model fo... | How to test for difference in means between 5 groups? The variance between the groups are not equal.
I would like to recommend generalized least squares as an option. Same way you can create a model for the mean of the data given your predictors, you can also create a model for variance. The gls() fu |
52,547 | How to test for difference in means between 5 groups? The variance between the groups are not equal. If they were equal, then I could use ANOVA | One of several possible methods is to use oneway.test in R.
Here is an example with three groups, each with ten observations:
x1 = rnorm(10, 100, 10); x2 = rnorm(10, 95, 15); x3 = rnorm(10, 90, 5)
x = c(x1, x2, x3); group = rep(1:3, each=10)
boxplot(x ~ group)
You can see that my fake data were generated with diffe... | How to test for difference in means between 5 groups? The variance between the groups are not equal. | One of several possible methods is to use oneway.test in R.
Here is an example with three groups, each with ten observations:
x1 = rnorm(10, 100, 10); x2 = rnorm(10, 95, 15); x3 = rnorm(10, 90, 5)
x | How to test for difference in means between 5 groups? The variance between the groups are not equal. If they were equal, then I could use ANOVA
One of several possible methods is to use oneway.test in R.
Here is an example with three groups, each with ten observations:
x1 = rnorm(10, 100, 10); x2 = rnorm(10, 95, 15); ... | How to test for difference in means between 5 groups? The variance between the groups are not equal.
One of several possible methods is to use oneway.test in R.
Here is an example with three groups, each with ten observations:
x1 = rnorm(10, 100, 10); x2 = rnorm(10, 95, 15); x3 = rnorm(10, 90, 5)
x |
52,548 | How to estimate the scale factor for MAD for a non-normal distribution? | Definition: In R, the MAD of a vector x of observations is
median(abs(x - median(x))) multiplied by the default constant you mention in your Question.
set.seed (726); x = round(rnorm(10, 100, 15)) # rounded-normal data
x
[1] 95 80 108 84 115 76 82 93 121 117
mad(x)
[1] 20.7564 # default MAD in ... | How to estimate the scale factor for MAD for a non-normal distribution? | Definition: In R, the MAD of a vector x of observations is
median(abs(x - median(x))) multiplied by the default constant you mention in your Question.
set.seed (726); x = round(rnorm(10, 100, 15)) # | How to estimate the scale factor for MAD for a non-normal distribution?
Definition: In R, the MAD of a vector x of observations is
median(abs(x - median(x))) multiplied by the default constant you mention in your Question.
set.seed (726); x = round(rnorm(10, 100, 15)) # rounded-normal data
x
[1] 95 80 108 84 115 7... | How to estimate the scale factor for MAD for a non-normal distribution?
Definition: In R, the MAD of a vector x of observations is
median(abs(x - median(x))) multiplied by the default constant you mention in your Question.
set.seed (726); x = round(rnorm(10, 100, 15)) # |
52,549 | Paired data comparison: regression or paired t-test? | Your t-test is answering the question you want, which is (in your own words) "check whether two methods (on average) yielded the same results", and on that side your analysis looks correct. This is simple, correct, and appropriate given your small sample size n=7.
Your regression model, however, is not set up to answer... | Paired data comparison: regression or paired t-test? | Your t-test is answering the question you want, which is (in your own words) "check whether two methods (on average) yielded the same results", and on that side your analysis looks correct. This is si | Paired data comparison: regression or paired t-test?
Your t-test is answering the question you want, which is (in your own words) "check whether two methods (on average) yielded the same results", and on that side your analysis looks correct. This is simple, correct, and appropriate given your small sample size n=7.
Yo... | Paired data comparison: regression or paired t-test?
Your t-test is answering the question you want, which is (in your own words) "check whether two methods (on average) yielded the same results", and on that side your analysis looks correct. This is si |
52,550 | Paired data comparison: regression or paired t-test? | The way you set up the regression in a "correlation style" does answer a different question (which is explained nicely by @olooney).
However, you can use regressions to test for mean differences. In the end this is what we call AN(C)OVAs. Similarly, the t-test for mean differences can be seen as a spacial case of the t... | Paired data comparison: regression or paired t-test? | The way you set up the regression in a "correlation style" does answer a different question (which is explained nicely by @olooney).
However, you can use regressions to test for mean differences. In t | Paired data comparison: regression or paired t-test?
The way you set up the regression in a "correlation style" does answer a different question (which is explained nicely by @olooney).
However, you can use regressions to test for mean differences. In the end this is what we call AN(C)OVAs. Similarly, the t-test for me... | Paired data comparison: regression or paired t-test?
The way you set up the regression in a "correlation style" does answer a different question (which is explained nicely by @olooney).
However, you can use regressions to test for mean differences. In t |
52,551 | Paired data comparison: regression or paired t-test? | Both methods answer slightly different questions. The t-test is all about means, the regression, as you used it, is about finding an optimal linear relationship. Of course, if the intercept is 0 and the slope is 1, then everything is easy. But what, if not?
x = runif(30, -5, 10)
y = jitter(1.2*x)
summary(lm(y~x))
The... | Paired data comparison: regression or paired t-test? | Both methods answer slightly different questions. The t-test is all about means, the regression, as you used it, is about finding an optimal linear relationship. Of course, if the intercept is 0 and t | Paired data comparison: regression or paired t-test?
Both methods answer slightly different questions. The t-test is all about means, the regression, as you used it, is about finding an optimal linear relationship. Of course, if the intercept is 0 and the slope is 1, then everything is easy. But what, if not?
x = runif... | Paired data comparison: regression or paired t-test?
Both methods answer slightly different questions. The t-test is all about means, the regression, as you used it, is about finding an optimal linear relationship. Of course, if the intercept is 0 and t |
52,552 | Bias induced from model selection | I believe what they are saying is if you use a hold out data for cross validation to estimate the generalization error of your model then you land up with the unbiased estimate of generalization error of the model.
But once you use that data set for selection process for a model, which I believe is tuning the model an... | Bias induced from model selection | I believe what they are saying is if you use a hold out data for cross validation to estimate the generalization error of your model then you land up with the unbiased estimate of generalization error | Bias induced from model selection
I believe what they are saying is if you use a hold out data for cross validation to estimate the generalization error of your model then you land up with the unbiased estimate of generalization error of the model.
But once you use that data set for selection process for a model, whic... | Bias induced from model selection
I believe what they are saying is if you use a hold out data for cross validation to estimate the generalization error of your model then you land up with the unbiased estimate of generalization error |
52,553 | Bias induced from model selection | When you evaluate a model it is assumed that your model is given apriori any seen data. As such model evaluation is fine considering the sample is representative. However when you choose a model based on data, the model fitting becomes a random variable estimation. Assessing performance on the same data is not unbiased... | Bias induced from model selection | When you evaluate a model it is assumed that your model is given apriori any seen data. As such model evaluation is fine considering the sample is representative. However when you choose a model based | Bias induced from model selection
When you evaluate a model it is assumed that your model is given apriori any seen data. As such model evaluation is fine considering the sample is representative. However when you choose a model based on data, the model fitting becomes a random variable estimation. Assessing performanc... | Bias induced from model selection
When you evaluate a model it is assumed that your model is given apriori any seen data. As such model evaluation is fine considering the sample is representative. However when you choose a model based |
52,554 | Bias induced from model selection | Below is my understanding of the paragraph (without having the context):
Start:
Cross-validation and information criteria make a correction for using the data twice (in constructing the posterior and in model assessment).
Cross-validation helps to avoid the so called "double-dipping" problem - when one uses the same ... | Bias induced from model selection | Below is my understanding of the paragraph (without having the context):
Start:
Cross-validation and information criteria make a correction for using the data twice (in constructing the posterior and | Bias induced from model selection
Below is my understanding of the paragraph (without having the context):
Start:
Cross-validation and information criteria make a correction for using the data twice (in constructing the posterior and in model assessment).
Cross-validation helps to avoid the so called "double-dipping"... | Bias induced from model selection
Below is my understanding of the paragraph (without having the context):
Start:
Cross-validation and information criteria make a correction for using the data twice (in constructing the posterior and |
52,555 | Bias induced from model selection | Cross validation (applied solely for validation/verification purposes) avoids the double use of cases being in the training set and in the test set for the same model. However, performance estimates that are used to select the apparently best of a variety of models are in fact part of model training. So cross validati... | Bias induced from model selection | Cross validation (applied solely for validation/verification purposes) avoids the double use of cases being in the training set and in the test set for the same model. However, performance estimates | Bias induced from model selection
Cross validation (applied solely for validation/verification purposes) avoids the double use of cases being in the training set and in the test set for the same model. However, performance estimates that are used to select the apparently best of a variety of models are in fact part of... | Bias induced from model selection
Cross validation (applied solely for validation/verification purposes) avoids the double use of cases being in the training set and in the test set for the same model. However, performance estimates |
52,556 | Yeo-Johnson and Logarithmic transformation | Almost. For a vector $U,$ the Yeo-Johnson with $\lambda=0$ is equivalent to the natural logarithm of $( U + 1 ).$ | Yeo-Johnson and Logarithmic transformation | Almost. For a vector $U,$ the Yeo-Johnson with $\lambda=0$ is equivalent to the natural logarithm of $( U + 1 ).$ | Yeo-Johnson and Logarithmic transformation
Almost. For a vector $U,$ the Yeo-Johnson with $\lambda=0$ is equivalent to the natural logarithm of $( U + 1 ).$ | Yeo-Johnson and Logarithmic transformation
Almost. For a vector $U,$ the Yeo-Johnson with $\lambda=0$ is equivalent to the natural logarithm of $( U + 1 ).$ |
52,557 | how to detect the exact size of an object in an image using machine learning? | This task of depth estimation is part of a hard and fundamental problem in computer vision called 3D reconstruction. Recovering metric information from images is sometimes called photogrammetry. It's hard because when you move from the real world to an image you lose information.
Specifically, the projective transform... | how to detect the exact size of an object in an image using machine learning? | This task of depth estimation is part of a hard and fundamental problem in computer vision called 3D reconstruction. Recovering metric information from images is sometimes called photogrammetry. It's | how to detect the exact size of an object in an image using machine learning?
This task of depth estimation is part of a hard and fundamental problem in computer vision called 3D reconstruction. Recovering metric information from images is sometimes called photogrammetry. It's hard because when you move from the real w... | how to detect the exact size of an object in an image using machine learning?
This task of depth estimation is part of a hard and fundamental problem in computer vision called 3D reconstruction. Recovering metric information from images is sometimes called photogrammetry. It's |
52,558 | how to detect the exact size of an object in an image using machine learning? | If you have enough labeled data, go for supervised learning with CNNs.
Try object detections such as YOLO. They give you the bounding box of the object, as well as the predicted class.
Some pre-trained models are also available, which in the latest version (YOLO9000!) supports around 9k classes. But not sure if your c... | how to detect the exact size of an object in an image using machine learning? | If you have enough labeled data, go for supervised learning with CNNs.
Try object detections such as YOLO. They give you the bounding box of the object, as well as the predicted class.
Some pre-train | how to detect the exact size of an object in an image using machine learning?
If you have enough labeled data, go for supervised learning with CNNs.
Try object detections such as YOLO. They give you the bounding box of the object, as well as the predicted class.
Some pre-trained models are also available, which in the... | how to detect the exact size of an object in an image using machine learning?
If you have enough labeled data, go for supervised learning with CNNs.
Try object detections such as YOLO. They give you the bounding box of the object, as well as the predicted class.
Some pre-train |
52,559 | Can sub-Gaussian distributions have non-zero mean? | It is standard in the bandit literature to abuse notation by considering a random variable $X$ to be $\sigma$-subgaussian if the noise $X - \mathbb{E}[X]$ is $\sigma$-subgaussian.
See the note on page 78 of Tor Lattimore and Csaba Szepesvari's book | Can sub-Gaussian distributions have non-zero mean? | It is standard in the bandit literature to abuse notation by considering a random variable $X$ to be $\sigma$-subgaussian if the noise $X - \mathbb{E}[X]$ is $\sigma$-subgaussian.
See the note on pag | Can sub-Gaussian distributions have non-zero mean?
It is standard in the bandit literature to abuse notation by considering a random variable $X$ to be $\sigma$-subgaussian if the noise $X - \mathbb{E}[X]$ is $\sigma$-subgaussian.
See the note on page 78 of Tor Lattimore and Csaba Szepesvari's book | Can sub-Gaussian distributions have non-zero mean?
It is standard in the bandit literature to abuse notation by considering a random variable $X$ to be $\sigma$-subgaussian if the noise $X - \mathbb{E}[X]$ is $\sigma$-subgaussian.
See the note on pag |
52,560 | Can sub-Gaussian distributions have non-zero mean? | The first comment on this question is incorrect strictly speaking; the proposition you link to shows that having zero mean is a necessary condition for being sub-Gaussian.
In some sense, you can still get a useful notion for non-centered random variables to be sub-Gaussian, but only if you change the definition.
If yo... | Can sub-Gaussian distributions have non-zero mean? | The first comment on this question is incorrect strictly speaking; the proposition you link to shows that having zero mean is a necessary condition for being sub-Gaussian.
In some sense, you can still | Can sub-Gaussian distributions have non-zero mean?
The first comment on this question is incorrect strictly speaking; the proposition you link to shows that having zero mean is a necessary condition for being sub-Gaussian.
In some sense, you can still get a useful notion for non-centered random variables to be sub-Gaus... | Can sub-Gaussian distributions have non-zero mean?
The first comment on this question is incorrect strictly speaking; the proposition you link to shows that having zero mean is a necessary condition for being sub-Gaussian.
In some sense, you can still |
52,561 | Average absolute value of a coordinate of a random unit vector? | This problem has a very nice geometrical interpretation if we can assume that the distribution $f(\vec{x})$ is constant over the surface of the $n-1$-unit-sphere in $n$-dimensional space. Then $f(\vec{x} \wedge (\vert x_i \vert=a))$ relates to the surface of two slices (at negative and positive coordinate) of the n-1 s... | Average absolute value of a coordinate of a random unit vector? | This problem has a very nice geometrical interpretation if we can assume that the distribution $f(\vec{x})$ is constant over the surface of the $n-1$-unit-sphere in $n$-dimensional space. Then $f(\vec | Average absolute value of a coordinate of a random unit vector?
This problem has a very nice geometrical interpretation if we can assume that the distribution $f(\vec{x})$ is constant over the surface of the $n-1$-unit-sphere in $n$-dimensional space. Then $f(\vec{x} \wedge (\vert x_i \vert=a))$ relates to the surface ... | Average absolute value of a coordinate of a random unit vector?
This problem has a very nice geometrical interpretation if we can assume that the distribution $f(\vec{x})$ is constant over the surface of the $n-1$-unit-sphere in $n$-dimensional space. Then $f(\vec |
52,562 | Average absolute value of a coordinate of a random unit vector? | The answer is $1/2$
This paper has the probability density $f_n(x_i)$ of $x_i$ for the vector inside an n-dimensional hypersphere. You're interested in the vector from origin to the random point on a surface of a hypersphere. To get the surface of a unit hypersphere you simply take a derivative along the radius then fi... | Average absolute value of a coordinate of a random unit vector? | The answer is $1/2$
This paper has the probability density $f_n(x_i)$ of $x_i$ for the vector inside an n-dimensional hypersphere. You're interested in the vector from origin to the random point on a | Average absolute value of a coordinate of a random unit vector?
The answer is $1/2$
This paper has the probability density $f_n(x_i)$ of $x_i$ for the vector inside an n-dimensional hypersphere. You're interested in the vector from origin to the random point on a surface of a hypersphere. To get the surface of a unit h... | Average absolute value of a coordinate of a random unit vector?
The answer is $1/2$
This paper has the probability density $f_n(x_i)$ of $x_i$ for the vector inside an n-dimensional hypersphere. You're interested in the vector from origin to the random point on a |
52,563 | In model selection with $Y$ as the outcome and $ X = (X_1, \ldots, X_p)$ the explanatory variables, why do we care about $F_{Y|X}$? | A regression model or a GLM (or indeed nay number of other models) are at heart a model of the conditional distribution, generally including an explicit description of the conditional mean in terms of the parameters.
When you're estimating parameters in (say) a linear regression, you're actually working out how (in yo... | In model selection with $Y$ as the outcome and $ X = (X_1, \ldots, X_p)$ the explanatory variables, | A regression model or a GLM (or indeed nay number of other models) are at heart a model of the conditional distribution, generally including an explicit description of the conditional mean in terms of | In model selection with $Y$ as the outcome and $ X = (X_1, \ldots, X_p)$ the explanatory variables, why do we care about $F_{Y|X}$?
A regression model or a GLM (or indeed nay number of other models) are at heart a model of the conditional distribution, generally including an explicit description of the conditional mean... | In model selection with $Y$ as the outcome and $ X = (X_1, \ldots, X_p)$ the explanatory variables,
A regression model or a GLM (or indeed nay number of other models) are at heart a model of the conditional distribution, generally including an explicit description of the conditional mean in terms of |
52,564 | In model selection with $Y$ as the outcome and $ X = (X_1, \ldots, X_p)$ the explanatory variables, why do we care about $F_{Y|X}$? | Suppose you want to build a predictive model. That is, you have some data $(X, Y)$, and you want to use knowledge of $X$ to make a prediction for the value of $Y$. Practically, you want to construct a function of $X$, so that $f(X)$ can be in some way construed as a "prediction for $Y$".
The thing you would most hope ... | In model selection with $Y$ as the outcome and $ X = (X_1, \ldots, X_p)$ the explanatory variables, | Suppose you want to build a predictive model. That is, you have some data $(X, Y)$, and you want to use knowledge of $X$ to make a prediction for the value of $Y$. Practically, you want to construct | In model selection with $Y$ as the outcome and $ X = (X_1, \ldots, X_p)$ the explanatory variables, why do we care about $F_{Y|X}$?
Suppose you want to build a predictive model. That is, you have some data $(X, Y)$, and you want to use knowledge of $X$ to make a prediction for the value of $Y$. Practically, you want t... | In model selection with $Y$ as the outcome and $ X = (X_1, \ldots, X_p)$ the explanatory variables,
Suppose you want to build a predictive model. That is, you have some data $(X, Y)$, and you want to use knowledge of $X$ to make a prediction for the value of $Y$. Practically, you want to construct |
52,565 | If the Pearson r is .1, is there a weak relationship between the two variables? | Let me again post the same quote from the web:
I once asked a chemist who was calibrating a laboratory instrument to
a standard what value of the correlation coefficient she was looking
for. “0.9 is too low. You need at least 0.98 or 0.99.” She got the
number from a government guidance document.
I once asked an... | If the Pearson r is .1, is there a weak relationship between the two variables? | Let me again post the same quote from the web:
I once asked a chemist who was calibrating a laboratory instrument to
a standard what value of the correlation coefficient she was looking
for. “0. | If the Pearson r is .1, is there a weak relationship between the two variables?
Let me again post the same quote from the web:
I once asked a chemist who was calibrating a laboratory instrument to
a standard what value of the correlation coefficient she was looking
for. “0.9 is too low. You need at least 0.98 or ... | If the Pearson r is .1, is there a weak relationship between the two variables?
Let me again post the same quote from the web:
I once asked a chemist who was calibrating a laboratory instrument to
a standard what value of the correlation coefficient she was looking
for. “0. |
52,566 | If the Pearson r is .1, is there a weak relationship between the two variables? | It depends on the sample size. If the sample size is small the estimate may not be significantly different from 0. On the other hand, if the sample size is large it may be statistically different from 0. In the latter case you might say that it is significant but to call it strong is a matter of judgement and depends ... | If the Pearson r is .1, is there a weak relationship between the two variables? | It depends on the sample size. If the sample size is small the estimate may not be significantly different from 0. On the other hand, if the sample size is large it may be statistically different fro | If the Pearson r is .1, is there a weak relationship between the two variables?
It depends on the sample size. If the sample size is small the estimate may not be significantly different from 0. On the other hand, if the sample size is large it may be statistically different from 0. In the latter case you might say th... | If the Pearson r is .1, is there a weak relationship between the two variables?
It depends on the sample size. If the sample size is small the estimate may not be significantly different from 0. On the other hand, if the sample size is large it may be statistically different fro |
52,567 | If the Pearson r is .1, is there a weak relationship between the two variables? | To add on the other answers, you might well also have a nonlinear dependency between the two variables that the Pearson's $r$ does not capture. Then you might have a look at the Maximal Information Coefficient MIC: here.
Anyway, the best thing you can probably do with two variables is to have a look at their scatter ... | If the Pearson r is .1, is there a weak relationship between the two variables? | To add on the other answers, you might well also have a nonlinear dependency between the two variables that the Pearson's $r$ does not capture. Then you might have a look at the Maximal Information C | If the Pearson r is .1, is there a weak relationship between the two variables?
To add on the other answers, you might well also have a nonlinear dependency between the two variables that the Pearson's $r$ does not capture. Then you might have a look at the Maximal Information Coefficient MIC: here.
Anyway, the best ... | If the Pearson r is .1, is there a weak relationship between the two variables?
To add on the other answers, you might well also have a nonlinear dependency between the two variables that the Pearson's $r$ does not capture. Then you might have a look at the Maximal Information C |
52,568 | Why would someone plot variance normalized by the mean? | Variance over mean is known as the Index of dispersion.
This can be useful when comparing two random variables with different means, in order to account for larger variance for larges means.
Example: suppose two fields have some sheep, and I hire 2 "counters" to count the sheep in each field. The counters count the she... | Why would someone plot variance normalized by the mean? | Variance over mean is known as the Index of dispersion.
This can be useful when comparing two random variables with different means, in order to account for larger variance for larges means.
Example: | Why would someone plot variance normalized by the mean?
Variance over mean is known as the Index of dispersion.
This can be useful when comparing two random variables with different means, in order to account for larger variance for larges means.
Example: suppose two fields have some sheep, and I hire 2 "counters" to c... | Why would someone plot variance normalized by the mean?
Variance over mean is known as the Index of dispersion.
This can be useful when comparing two random variables with different means, in order to account for larger variance for larges means.
Example: |
52,569 | t test with drastically different sample sizes [duplicate] | The Welch approximation t-test is designed to do the same thing as an independent samples t-test, but without relying on the assumption that the variances are equal. It is readily available in most standard statistical software. In R, it's actually the default for the t.test function (the argument var.equal controls wh... | t test with drastically different sample sizes [duplicate] | The Welch approximation t-test is designed to do the same thing as an independent samples t-test, but without relying on the assumption that the variances are equal. It is readily available in most st | t test with drastically different sample sizes [duplicate]
The Welch approximation t-test is designed to do the same thing as an independent samples t-test, but without relying on the assumption that the variances are equal. It is readily available in most standard statistical software. In R, it's actually the default ... | t test with drastically different sample sizes [duplicate]
The Welch approximation t-test is designed to do the same thing as an independent samples t-test, but without relying on the assumption that the variances are equal. It is readily available in most st |
52,570 | t test with drastically different sample sizes [duplicate] | The t-test is not dependent on equal, similar, or even close sample sizes. A t-test can be done with any sample sizes. Go ahead and use the t-test you have. I wish I knew where people got the idea that a t-test requires equal sample sizes. | t test with drastically different sample sizes [duplicate] | The t-test is not dependent on equal, similar, or even close sample sizes. A t-test can be done with any sample sizes. Go ahead and use the t-test you have. I wish I knew where people got the idea tha | t test with drastically different sample sizes [duplicate]
The t-test is not dependent on equal, similar, or even close sample sizes. A t-test can be done with any sample sizes. Go ahead and use the t-test you have. I wish I knew where people got the idea that a t-test requires equal sample sizes. | t test with drastically different sample sizes [duplicate]
The t-test is not dependent on equal, similar, or even close sample sizes. A t-test can be done with any sample sizes. Go ahead and use the t-test you have. I wish I knew where people got the idea tha |
52,571 | What is the probability of selecting all the blue balls? | This can be reduced to a combinatorics problem. Let's make it a little more general.
Suppose you have $n$ balls, of which $r$ are blue. You select $k,$ where $k > r.$
What are the total number of ways you can select $k$ balls out of $n?$
Then, what are the total number of ways you can select $k$ balls out of $n,$ wher... | What is the probability of selecting all the blue balls? | This can be reduced to a combinatorics problem. Let's make it a little more general.
Suppose you have $n$ balls, of which $r$ are blue. You select $k,$ where $k > r.$
What are the total number of way | What is the probability of selecting all the blue balls?
This can be reduced to a combinatorics problem. Let's make it a little more general.
Suppose you have $n$ balls, of which $r$ are blue. You select $k,$ where $k > r.$
What are the total number of ways you can select $k$ balls out of $n?$
Then, what are the total... | What is the probability of selecting all the blue balls?
This can be reduced to a combinatorics problem. Let's make it a little more general.
Suppose you have $n$ balls, of which $r$ are blue. You select $k,$ where $k > r.$
What are the total number of way |
52,572 | What is the probability of selecting all the blue balls? | It's a typical brain teaser. Invert the question: what is the probability that none of the blue balls are scooped out of the bag?
All of a sudden it's easy to answer! $$\frac{n-r}{n}\frac{n-r-1}{n-1}\dots\frac{n-m+1-r}{n-m+1}=\frac{(n-m)!(n-r)!}{n!(n-r-m)!}$$
You pull the first ball, and it's not blue. How likely it is... | What is the probability of selecting all the blue balls? | It's a typical brain teaser. Invert the question: what is the probability that none of the blue balls are scooped out of the bag?
All of a sudden it's easy to answer! $$\frac{n-r}{n}\frac{n-r-1}{n-1}\ | What is the probability of selecting all the blue balls?
It's a typical brain teaser. Invert the question: what is the probability that none of the blue balls are scooped out of the bag?
All of a sudden it's easy to answer! $$\frac{n-r}{n}\frac{n-r-1}{n-1}\dots\frac{n-m+1-r}{n-m+1}=\frac{(n-m)!(n-r)!}{n!(n-r-m)!}$$
You... | What is the probability of selecting all the blue balls?
It's a typical brain teaser. Invert the question: what is the probability that none of the blue balls are scooped out of the bag?
All of a sudden it's easy to answer! $$\frac{n-r}{n}\frac{n-r-1}{n-1}\ |
52,573 | Notation for two expressions with the same distribution | Notation : $\cos(U) \stackrel d=\sin(U)$
If $X$ and $Y$ follow same distribution then mathematically you can write $X \stackrel d=Y$. | Notation for two expressions with the same distribution | Notation : $\cos(U) \stackrel d=\sin(U)$
If $X$ and $Y$ follow same distribution then mathematically you can write $X \stackrel d=Y$. | Notation for two expressions with the same distribution
Notation : $\cos(U) \stackrel d=\sin(U)$
If $X$ and $Y$ follow same distribution then mathematically you can write $X \stackrel d=Y$. | Notation for two expressions with the same distribution
Notation : $\cos(U) \stackrel d=\sin(U)$
If $X$ and $Y$ follow same distribution then mathematically you can write $X \stackrel d=Y$. |
52,574 | Is it valid to do a test only on most extreme subjects, instead of everybody? | Since you raise pre-registering a procedure in comments I thought I'd post a brief discussion related to it. Let's imagine you can avoid all of the pitfalls in the Garden of forking paths paper linked in another answer.
So we're at the point of that choices of what procedures to use. In what follows I'll make a number ... | Is it valid to do a test only on most extreme subjects, instead of everybody? | Since you raise pre-registering a procedure in comments I thought I'd post a brief discussion related to it. Let's imagine you can avoid all of the pitfalls in the Garden of forking paths paper linked | Is it valid to do a test only on most extreme subjects, instead of everybody?
Since you raise pre-registering a procedure in comments I thought I'd post a brief discussion related to it. Let's imagine you can avoid all of the pitfalls in the Garden of forking paths paper linked in another answer.
So we're at the point ... | Is it valid to do a test only on most extreme subjects, instead of everybody?
Since you raise pre-registering a procedure in comments I thought I'd post a brief discussion related to it. Let's imagine you can avoid all of the pitfalls in the Garden of forking paths paper linked |
52,575 | Is it valid to do a test only on most extreme subjects, instead of everybody? | This is not valid. People are only going onto the t-tests because the regression failed to yield a significant result. Andrew Gelman refers to these choices as the "garden of forking paths," and if a researcher does enough things to the data in search of p < .05, the Type I error rate can be greatly inflated.
Dichotomi... | Is it valid to do a test only on most extreme subjects, instead of everybody? | This is not valid. People are only going onto the t-tests because the regression failed to yield a significant result. Andrew Gelman refers to these choices as the "garden of forking paths," and if a | Is it valid to do a test only on most extreme subjects, instead of everybody?
This is not valid. People are only going onto the t-tests because the regression failed to yield a significant result. Andrew Gelman refers to these choices as the "garden of forking paths," and if a researcher does enough things to the data ... | Is it valid to do a test only on most extreme subjects, instead of everybody?
This is not valid. People are only going onto the t-tests because the regression failed to yield a significant result. Andrew Gelman refers to these choices as the "garden of forking paths," and if a |
52,576 | Is it valid to do a test only on most extreme subjects, instead of everybody? | I would comment if I could, but you may find this What is the benefit of breaking up a continuous predictor variable? useful -- Scorthi's answer in particular.
Also this http://biostat.mc.vanderbilt.edu/wiki/Main/CatContinuous for a list of problems caused by categorising a continuous variable.
To me what you describe ... | Is it valid to do a test only on most extreme subjects, instead of everybody? | I would comment if I could, but you may find this What is the benefit of breaking up a continuous predictor variable? useful -- Scorthi's answer in particular.
Also this http://biostat.mc.vanderbilt.e | Is it valid to do a test only on most extreme subjects, instead of everybody?
I would comment if I could, but you may find this What is the benefit of breaking up a continuous predictor variable? useful -- Scorthi's answer in particular.
Also this http://biostat.mc.vanderbilt.edu/wiki/Main/CatContinuous for a list of p... | Is it valid to do a test only on most extreme subjects, instead of everybody?
I would comment if I could, but you may find this What is the benefit of breaking up a continuous predictor variable? useful -- Scorthi's answer in particular.
Also this http://biostat.mc.vanderbilt.e |
52,577 | Logistic regression with poor goodness of fit (hosmer lemeshow)? | The Hosmer and Lemeshow test is obsolete as has been discussed elsewhere on this site. See also Goodness-of-fit test in Logistic regression; which 'fit' do we want to test?.
My Regression Modeling Strategies course notes at https://hbiostat.org/rms present a hopefully coherent strategy for logistic regression model sp... | Logistic regression with poor goodness of fit (hosmer lemeshow)? | The Hosmer and Lemeshow test is obsolete as has been discussed elsewhere on this site. See also Goodness-of-fit test in Logistic regression; which 'fit' do we want to test?.
My Regression Modeling St | Logistic regression with poor goodness of fit (hosmer lemeshow)?
The Hosmer and Lemeshow test is obsolete as has been discussed elsewhere on this site. See also Goodness-of-fit test in Logistic regression; which 'fit' do we want to test?.
My Regression Modeling Strategies course notes at https://hbiostat.org/rms prese... | Logistic regression with poor goodness of fit (hosmer lemeshow)?
The Hosmer and Lemeshow test is obsolete as has been discussed elsewhere on this site. See also Goodness-of-fit test in Logistic regression; which 'fit' do we want to test?.
My Regression Modeling St |
52,578 | Motivation for average log-likelihood | TLDR version:
If you are using a first order optimization algorithm, such as gradient ascent, using the average likelihood as your objective function stabilizes the behavior of algorithm as the sample size changes. On the other hand, if you are using a second order optimization algorithm, such as Newton's Method, wheth... | Motivation for average log-likelihood | TLDR version:
If you are using a first order optimization algorithm, such as gradient ascent, using the average likelihood as your objective function stabilizes the behavior of algorithm as the sample | Motivation for average log-likelihood
TLDR version:
If you are using a first order optimization algorithm, such as gradient ascent, using the average likelihood as your objective function stabilizes the behavior of algorithm as the sample size changes. On the other hand, if you are using a second order optimization alg... | Motivation for average log-likelihood
TLDR version:
If you are using a first order optimization algorithm, such as gradient ascent, using the average likelihood as your objective function stabilizes the behavior of algorithm as the sample |
52,579 | Motivation for average log-likelihood | One reason to divide by $N$ would be to make numbers comparable over data sets with different sample sizes. Otherwise it does not seem a very important issue. | Motivation for average log-likelihood | One reason to divide by $N$ would be to make numbers comparable over data sets with different sample sizes. Otherwise it does not seem a very important issue. | Motivation for average log-likelihood
One reason to divide by $N$ would be to make numbers comparable over data sets with different sample sizes. Otherwise it does not seem a very important issue. | Motivation for average log-likelihood
One reason to divide by $N$ would be to make numbers comparable over data sets with different sample sizes. Otherwise it does not seem a very important issue. |
52,580 | How to test the statistical hypothesis that data was generated from a multinomial distribution? | This looks like a goodness-of-fit application to me. You should use the chi-square test. So if you have 3 sides and your probability vector is (0.1, 0.2, 0.7), and you have 100 trials. You would expect the outcomes be (10, 20, 70). Use the theoretical counts to compare with your observed counts in the chi-square test.
... | How to test the statistical hypothesis that data was generated from a multinomial distribution? | This looks like a goodness-of-fit application to me. You should use the chi-square test. So if you have 3 sides and your probability vector is (0.1, 0.2, 0.7), and you have 100 trials. You would expec | How to test the statistical hypothesis that data was generated from a multinomial distribution?
This looks like a goodness-of-fit application to me. You should use the chi-square test. So if you have 3 sides and your probability vector is (0.1, 0.2, 0.7), and you have 100 trials. You would expect the outcomes be (10, 2... | How to test the statistical hypothesis that data was generated from a multinomial distribution?
This looks like a goodness-of-fit application to me. You should use the chi-square test. So if you have 3 sides and your probability vector is (0.1, 0.2, 0.7), and you have 100 trials. You would expec |
52,581 | How to test the statistical hypothesis that data was generated from a multinomial distribution? | The existing answers point out Pearson's chi-squared test. Though this is usually a fine solution, it does rely on an approximation. Pearson derived that the chi-squared statistic approximately follows a chi-squared distribution, which he used to calculate p values. He did this derivation by assuming that the multinomi... | How to test the statistical hypothesis that data was generated from a multinomial distribution? | The existing answers point out Pearson's chi-squared test. Though this is usually a fine solution, it does rely on an approximation. Pearson derived that the chi-squared statistic approximately follow | How to test the statistical hypothesis that data was generated from a multinomial distribution?
The existing answers point out Pearson's chi-squared test. Though this is usually a fine solution, it does rely on an approximation. Pearson derived that the chi-squared statistic approximately follows a chi-squared distribu... | How to test the statistical hypothesis that data was generated from a multinomial distribution?
The existing answers point out Pearson's chi-squared test. Though this is usually a fine solution, it does rely on an approximation. Pearson derived that the chi-squared statistic approximately follow |
52,582 | How to test the statistical hypothesis that data was generated from a multinomial distribution? | Yes, it's called a Pearson's $\chi^2$ test. The expected frequencies are $E_i = N \times p_i$ (where $N$ is the total sample size) and the observed frequencies are what you called $n_1, ..., n_k$. | How to test the statistical hypothesis that data was generated from a multinomial distribution? | Yes, it's called a Pearson's $\chi^2$ test. The expected frequencies are $E_i = N \times p_i$ (where $N$ is the total sample size) and the observed frequencies are what you called $n_1, ..., n_k$. | How to test the statistical hypothesis that data was generated from a multinomial distribution?
Yes, it's called a Pearson's $\chi^2$ test. The expected frequencies are $E_i = N \times p_i$ (where $N$ is the total sample size) and the observed frequencies are what you called $n_1, ..., n_k$. | How to test the statistical hypothesis that data was generated from a multinomial distribution?
Yes, it's called a Pearson's $\chi^2$ test. The expected frequencies are $E_i = N \times p_i$ (where $N$ is the total sample size) and the observed frequencies are what you called $n_1, ..., n_k$. |
52,583 | How to test the statistical hypothesis that data was generated from a multinomial distribution? | The application of the goodness of fit tests is the wrong solutions because they reject the hypothesis, which you like to confirm. The right technique the equivalence testing. Please, look at my papers https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2907258 and https://www.researchgate.net/publication/312481284_Tes... | How to test the statistical hypothesis that data was generated from a multinomial distribution? | The application of the goodness of fit tests is the wrong solutions because they reject the hypothesis, which you like to confirm. The right technique the equivalence testing. Please, look at my paper | How to test the statistical hypothesis that data was generated from a multinomial distribution?
The application of the goodness of fit tests is the wrong solutions because they reject the hypothesis, which you like to confirm. The right technique the equivalence testing. Please, look at my papers https://papers.ssrn.co... | How to test the statistical hypothesis that data was generated from a multinomial distribution?
The application of the goodness of fit tests is the wrong solutions because they reject the hypothesis, which you like to confirm. The right technique the equivalence testing. Please, look at my paper |
52,584 | Things that I am not sure about "LASSO" regression method | For the first question, recall that in centering we replace each value $y_i$ with $y_i - \bar y$, where $\bar y$ is the mean of the $y$ vector. Then
$$ \sum_i (y_i - \bar y) = \sum_i y_i - n \bar y = \sum_i y_i - \sum_i y_i = 0 $$
I would like to make sure, is the reason of $ \bar y $ equals zero because $ \bar y = \... | Things that I am not sure about "LASSO" regression method | For the first question, recall that in centering we replace each value $y_i$ with $y_i - \bar y$, where $\bar y$ is the mean of the $y$ vector. Then
$$ \sum_i (y_i - \bar y) = \sum_i y_i - n \bar y = | Things that I am not sure about "LASSO" regression method
For the first question, recall that in centering we replace each value $y_i$ with $y_i - \bar y$, where $\bar y$ is the mean of the $y$ vector. Then
$$ \sum_i (y_i - \bar y) = \sum_i y_i - n \bar y = \sum_i y_i - \sum_i y_i = 0 $$
I would like to make sure, is... | Things that I am not sure about "LASSO" regression method
For the first question, recall that in centering we replace each value $y_i$ with $y_i - \bar y$, where $\bar y$ is the mean of the $y$ vector. Then
$$ \sum_i (y_i - \bar y) = \sum_i y_i - n \bar y = |
52,585 | Can you test for normality for a (0,1) bounded distribution? | It makes about as much sense to test these data for Normality (specifically, to compute some test statistic and compare it against the distribution of the test statistic expected for samples that truly came from a Normal distribution) as it ever does. If this kind of test is a usual part of your workflow for other data... | Can you test for normality for a (0,1) bounded distribution? | It makes about as much sense to test these data for Normality (specifically, to compute some test statistic and compare it against the distribution of the test statistic expected for samples that trul | Can you test for normality for a (0,1) bounded distribution?
It makes about as much sense to test these data for Normality (specifically, to compute some test statistic and compare it against the distribution of the test statistic expected for samples that truly came from a Normal distribution) as it ever does. If this... | Can you test for normality for a (0,1) bounded distribution?
It makes about as much sense to test these data for Normality (specifically, to compute some test statistic and compare it against the distribution of the test statistic expected for samples that trul |
52,586 | Understanding the solution of this integral | Integrals are linear:
$$\int_{z^*}^\infty \left(S_t\, e^{\mu\tau-\sigma^2\tau/2+\sigma\sqrt{\tau}z}\right)\frac{1}{\sqrt{2\pi}}e^{-\frac{z^2}{2}}dz
=\color{blue}{\left( S_t\, e^{\mu\tau-\sigma^2\tau/2}\right)}\frac{1}{\sqrt{2\pi}}\int_{z^*}^\infty e^{\sigma\sqrt{\tau}z-\frac{z^2}{2}}dz.$$
The exponent in the integrand... | Understanding the solution of this integral | Integrals are linear:
$$\int_{z^*}^\infty \left(S_t\, e^{\mu\tau-\sigma^2\tau/2+\sigma\sqrt{\tau}z}\right)\frac{1}{\sqrt{2\pi}}e^{-\frac{z^2}{2}}dz
=\color{blue}{\left( S_t\, e^{\mu\tau-\sigma^2\tau/ | Understanding the solution of this integral
Integrals are linear:
$$\int_{z^*}^\infty \left(S_t\, e^{\mu\tau-\sigma^2\tau/2+\sigma\sqrt{\tau}z}\right)\frac{1}{\sqrt{2\pi}}e^{-\frac{z^2}{2}}dz
=\color{blue}{\left( S_t\, e^{\mu\tau-\sigma^2\tau/2}\right)}\frac{1}{\sqrt{2\pi}}\int_{z^*}^\infty e^{\sigma\sqrt{\tau}z-\frac... | Understanding the solution of this integral
Integrals are linear:
$$\int_{z^*}^\infty \left(S_t\, e^{\mu\tau-\sigma^2\tau/2+\sigma\sqrt{\tau}z}\right)\frac{1}{\sqrt{2\pi}}e^{-\frac{z^2}{2}}dz
=\color{blue}{\left( S_t\, e^{\mu\tau-\sigma^2\tau/ |
52,587 | Granger Causality vs. Forecasting | Granger causality tells you that variable $X$ provides helpful information about future values of $Y$ <...>
The devil is in the details. Granger causality considers the incremental benefits on forecasting $Y$ due to using the history of $X$ extra to using the history of $Y$ alone. That is, the benchmark forecast is ba... | Granger Causality vs. Forecasting | Granger causality tells you that variable $X$ provides helpful information about future values of $Y$ <...>
The devil is in the details. Granger causality considers the incremental benefits on foreca | Granger Causality vs. Forecasting
Granger causality tells you that variable $X$ provides helpful information about future values of $Y$ <...>
The devil is in the details. Granger causality considers the incremental benefits on forecasting $Y$ due to using the history of $X$ extra to using the history of $Y$ alone. Tha... | Granger Causality vs. Forecasting
Granger causality tells you that variable $X$ provides helpful information about future values of $Y$ <...>
The devil is in the details. Granger causality considers the incremental benefits on foreca |
52,588 | Granger Causality vs. Forecasting | Granger causality is a weak form of causal inference, particularly when compared with Pearl-type causality and Bayesian networks. Forecasts, on the other hand, make no assumptions about possible causal relationships and, given that, demonstrate association for the purposes of prediction. | Granger Causality vs. Forecasting | Granger causality is a weak form of causal inference, particularly when compared with Pearl-type causality and Bayesian networks. Forecasts, on the other hand, make no assumptions about possible causa | Granger Causality vs. Forecasting
Granger causality is a weak form of causal inference, particularly when compared with Pearl-type causality and Bayesian networks. Forecasts, on the other hand, make no assumptions about possible causal relationships and, given that, demonstrate association for the purposes of predictio... | Granger Causality vs. Forecasting
Granger causality is a weak form of causal inference, particularly when compared with Pearl-type causality and Bayesian networks. Forecasts, on the other hand, make no assumptions about possible causa |
52,589 | Why 0 for failure and 1 for success in a Bernoulli distribution? | As already noted by Mark L. Stone, it is used because of tradition and convenience. It could have been $-1$ and $+1$ as with Rademacher distribution, or any other values.
However there are also other reasons that make $0$ and $1$ a convenient choice. First, expected value of Bernoulli distributed random variable is
$$ ... | Why 0 for failure and 1 for success in a Bernoulli distribution? | As already noted by Mark L. Stone, it is used because of tradition and convenience. It could have been $-1$ and $+1$ as with Rademacher distribution, or any other values.
However there are also other | Why 0 for failure and 1 for success in a Bernoulli distribution?
As already noted by Mark L. Stone, it is used because of tradition and convenience. It could have been $-1$ and $+1$ as with Rademacher distribution, or any other values.
However there are also other reasons that make $0$ and $1$ a convenient choice. Firs... | Why 0 for failure and 1 for success in a Bernoulli distribution?
As already noted by Mark L. Stone, it is used because of tradition and convenience. It could have been $-1$ and $+1$ as with Rademacher distribution, or any other values.
However there are also other |
52,590 | Why 0 for failure and 1 for success in a Bernoulli distribution? | Mathematical convenience. Here is an example: if you set the success case to be $1$ and the failure case to be $0$, then you have that the binomial variable $X \sim B(n, p)$, which counts the number of successes in $n$ independent Bernoulli trials $X_i \sim B(1, p)$, with $i = 1, 2, ..., n$, can be written as
$$ X = \s... | Why 0 for failure and 1 for success in a Bernoulli distribution? | Mathematical convenience. Here is an example: if you set the success case to be $1$ and the failure case to be $0$, then you have that the binomial variable $X \sim B(n, p)$, which counts the number o | Why 0 for failure and 1 for success in a Bernoulli distribution?
Mathematical convenience. Here is an example: if you set the success case to be $1$ and the failure case to be $0$, then you have that the binomial variable $X \sim B(n, p)$, which counts the number of successes in $n$ independent Bernoulli trials $X_i \s... | Why 0 for failure and 1 for success in a Bernoulli distribution?
Mathematical convenience. Here is an example: if you set the success case to be $1$ and the failure case to be $0$, then you have that the binomial variable $X \sim B(n, p)$, which counts the number o |
52,591 | Two-way ANOVA vs ANCOVA in R | Order matters whenever the predictors aren't independent. They're correlated in your first example, as they're continuous measurements on each of the diamonds, but not in the second, as those are assigned in a balanced way.
ANOVA/ANCOVA/regression are all names for linear models; they do exactly the same thing mathemat... | Two-way ANOVA vs ANCOVA in R | Order matters whenever the predictors aren't independent. They're correlated in your first example, as they're continuous measurements on each of the diamonds, but not in the second, as those are assi | Two-way ANOVA vs ANCOVA in R
Order matters whenever the predictors aren't independent. They're correlated in your first example, as they're continuous measurements on each of the diamonds, but not in the second, as those are assigned in a balanced way.
ANOVA/ANCOVA/regression are all names for linear models; they do ex... | Two-way ANOVA vs ANCOVA in R
Order matters whenever the predictors aren't independent. They're correlated in your first example, as they're continuous measurements on each of the diamonds, but not in the second, as those are assi |
52,592 | Two-way ANOVA vs ANCOVA in R | Stumbled on this question a couple of years after it was posted while looking for some info on ANCOVA with R. Wound up writing a much longer example using the diamonds dataset I won't try and cram it in here but for future searchers it is located here: https://ibecav.github.io/ancova_example/ .
I would answer your 3 o... | Two-way ANOVA vs ANCOVA in R | Stumbled on this question a couple of years after it was posted while looking for some info on ANCOVA with R. Wound up writing a much longer example using the diamonds dataset I won't try and cram it | Two-way ANOVA vs ANCOVA in R
Stumbled on this question a couple of years after it was posted while looking for some info on ANCOVA with R. Wound up writing a much longer example using the diamonds dataset I won't try and cram it in here but for future searchers it is located here: https://ibecav.github.io/ancova_examp... | Two-way ANOVA vs ANCOVA in R
Stumbled on this question a couple of years after it was posted while looking for some info on ANCOVA with R. Wound up writing a much longer example using the diamonds dataset I won't try and cram it |
52,593 | Can lavaan (SEM/CFA) be used to do factor analysis like factanal (EFA) | It is possible to do EFA in a CFA framework. This is sometimes called "E/CFA". A nice discussion of this can be found in:
Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: Guilford Press.
For this to work, you need to have an "anchor item" for each factor, for which there are no cross-lo... | Can lavaan (SEM/CFA) be used to do factor analysis like factanal (EFA) | It is possible to do EFA in a CFA framework. This is sometimes called "E/CFA". A nice discussion of this can be found in:
Brown, T. A. (2006). Confirmatory factor analysis for applied research. New Yo | Can lavaan (SEM/CFA) be used to do factor analysis like factanal (EFA)
It is possible to do EFA in a CFA framework. This is sometimes called "E/CFA". A nice discussion of this can be found in:
Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: Guilford Press.
For this to work, you need to... | Can lavaan (SEM/CFA) be used to do factor analysis like factanal (EFA)
It is possible to do EFA in a CFA framework. This is sometimes called "E/CFA". A nice discussion of this can be found in:
Brown, T. A. (2006). Confirmatory factor analysis for applied research. New Yo |
52,594 | How to read a boxplot in R? [duplicate] | The documentation seems fairly clear to me, although it certainly helps to be familiar with how to read R documentation and with boxplots more generally. Towards the bottom of the page it says:
See Also
boxplot.stats which does the computation...
So we can navigate there. It reads:
Details
The two ‘hinges’ are ver... | How to read a boxplot in R? [duplicate] | The documentation seems fairly clear to me, although it certainly helps to be familiar with how to read R documentation and with boxplots more generally. Towards the bottom of the page it says:
See | How to read a boxplot in R? [duplicate]
The documentation seems fairly clear to me, although it certainly helps to be familiar with how to read R documentation and with boxplots more generally. Towards the bottom of the page it says:
See Also
boxplot.stats which does the computation...
So we can navigate there. It ... | How to read a boxplot in R? [duplicate]
The documentation seems fairly clear to me, although it certainly helps to be familiar with how to read R documentation and with boxplots more generally. Towards the bottom of the page it says:
See |
52,595 | How to read a boxplot in R? [duplicate] | This sums up the box plot and what each line represents.
Source:
http://www.physics.csbsju.edu/stats/box2.html | How to read a boxplot in R? [duplicate] | This sums up the box plot and what each line represents.
Source:
http://www.physics.csbsju.edu/stats/box2.html | How to read a boxplot in R? [duplicate]
This sums up the box plot and what each line represents.
Source:
http://www.physics.csbsju.edu/stats/box2.html | How to read a boxplot in R? [duplicate]
This sums up the box plot and what each line represents.
Source:
http://www.physics.csbsju.edu/stats/box2.html |
52,596 | What does "linear-by-linear association" in SPSS mean? | It is. You might have a look at IBM's support page for SPSS,
where it is stated in a technote on the Chi² test:
'The Crosstabs procedure includes the Mantel-Haenszel test of trend among its chi-square test statistics. ... The MH test for trend will be printed in the "Chi-Square Tests" table and labelled "Linear-by-Line... | What does "linear-by-linear association" in SPSS mean? | It is. You might have a look at IBM's support page for SPSS,
where it is stated in a technote on the Chi² test:
'The Crosstabs procedure includes the Mantel-Haenszel test of trend among its chi-square | What does "linear-by-linear association" in SPSS mean?
It is. You might have a look at IBM's support page for SPSS,
where it is stated in a technote on the Chi² test:
'The Crosstabs procedure includes the Mantel-Haenszel test of trend among its chi-square test statistics. ... The MH test for trend will be printed in th... | What does "linear-by-linear association" in SPSS mean?
It is. You might have a look at IBM's support page for SPSS,
where it is stated in a technote on the Chi² test:
'The Crosstabs procedure includes the Mantel-Haenszel test of trend among its chi-square |
52,597 | What does "linear-by-linear association" in SPSS mean? | As a previous reply mentioned, yes it is and the technical description is at SPSS's support page: https://www-304.ibm.com/support/docview.wss?uid=swg21477269
This is a useful statistic for those who understand it. Suppose we investigate whether 78 employees' promotion (yes/no) is related to their performance ranking i... | What does "linear-by-linear association" in SPSS mean? | As a previous reply mentioned, yes it is and the technical description is at SPSS's support page: https://www-304.ibm.com/support/docview.wss?uid=swg21477269
This is a useful statistic for those who u | What does "linear-by-linear association" in SPSS mean?
As a previous reply mentioned, yes it is and the technical description is at SPSS's support page: https://www-304.ibm.com/support/docview.wss?uid=swg21477269
This is a useful statistic for those who understand it. Suppose we investigate whether 78 employees' promo... | What does "linear-by-linear association" in SPSS mean?
As a previous reply mentioned, yes it is and the technical description is at SPSS's support page: https://www-304.ibm.com/support/docview.wss?uid=swg21477269
This is a useful statistic for those who u |
52,598 | How to write a piecewise regression model as a linear model? | The overall model has four parameters: $\alpha_0,$ $\alpha_1,$ $\beta_0,$ and $\beta_1.$ Therefore, if a solution is at all possible, we must be able to construct four corresponding variables $z_1, z_2,$ $z_3,$ and $z_4.$
One solution dedicates the first two parameters to the first model and the second two parameters ... | How to write a piecewise regression model as a linear model? | The overall model has four parameters: $\alpha_0,$ $\alpha_1,$ $\beta_0,$ and $\beta_1.$ Therefore, if a solution is at all possible, we must be able to construct four corresponding variables $z_1, z | How to write a piecewise regression model as a linear model?
The overall model has four parameters: $\alpha_0,$ $\alpha_1,$ $\beta_0,$ and $\beta_1.$ Therefore, if a solution is at all possible, we must be able to construct four corresponding variables $z_1, z_2,$ $z_3,$ and $z_4.$
One solution dedicates the first two... | How to write a piecewise regression model as a linear model?
The overall model has four parameters: $\alpha_0,$ $\alpha_1,$ $\beta_0,$ and $\beta_1.$ Therefore, if a solution is at all possible, we must be able to construct four corresponding variables $z_1, z |
52,599 | How to write a piecewise regression model as a linear model? | For a known discontinuous break point $x_0$, the following piecewise regression model:
$$y= \alpha_0 + \alpha_1 x +\epsilon ;\ \ x\le x_0 $$
$$y=\beta_0 +\beta_1 x + \epsilon;\ \ x\gt x_0$$
can instead be expressed using an indicator function of $x$ and $x_0$ for the change in intercept, and a hinge function of $x_i$ ... | How to write a piecewise regression model as a linear model? | For a known discontinuous break point $x_0$, the following piecewise regression model:
$$y= \alpha_0 + \alpha_1 x +\epsilon ;\ \ x\le x_0 $$
$$y=\beta_0 +\beta_1 x + \epsilon;\ \ x\gt x_0$$
can inste | How to write a piecewise regression model as a linear model?
For a known discontinuous break point $x_0$, the following piecewise regression model:
$$y= \alpha_0 + \alpha_1 x +\epsilon ;\ \ x\le x_0 $$
$$y=\beta_0 +\beta_1 x + \epsilon;\ \ x\gt x_0$$
can instead be expressed using an indicator function of $x$ and $x_0... | How to write a piecewise regression model as a linear model?
For a known discontinuous break point $x_0$, the following piecewise regression model:
$$y= \alpha_0 + \alpha_1 x +\epsilon ;\ \ x\le x_0 $$
$$y=\beta_0 +\beta_1 x + \epsilon;\ \ x\gt x_0$$
can inste |
52,600 | Linear regression performing better than random forest in Caret | Definitely check on how $R^2$ is being evaluated and whether it is uniform across the different algorithms. Beyond that, a few thoughts occur to me:
If your features have a smooth, nearly linear dependence on the covariates, then linear regression will model the dependence better than random forests, which will basica... | Linear regression performing better than random forest in Caret | Definitely check on how $R^2$ is being evaluated and whether it is uniform across the different algorithms. Beyond that, a few thoughts occur to me:
If your features have a smooth, nearly linear depe | Linear regression performing better than random forest in Caret
Definitely check on how $R^2$ is being evaluated and whether it is uniform across the different algorithms. Beyond that, a few thoughts occur to me:
If your features have a smooth, nearly linear dependence on the covariates, then linear regression will mo... | Linear regression performing better than random forest in Caret
Definitely check on how $R^2$ is being evaluated and whether it is uniform across the different algorithms. Beyond that, a few thoughts occur to me:
If your features have a smooth, nearly linear depe |
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